Aeronautical structures are mainly composed of composite panels 1 (FIG. 1) which are generally composed of skins 3 reinforced in the longitudinal and orbital directions by strengtheners 2 respectively designated as stringers and frames, for example. The presence of these strengtheners is aimed at protecting the structure from buckling and at limiting the propagation of cracks.
Such panels are mainly composed of composite materials having particularly interesting properties for many industries. As a matter of fact, they have a great mechanical and thermal resistance in spite of a low mass, and they also allow for large design freedom and easy maintenance.
Composite materials are generally composed of reinforcing fibres buried in a polymer matrix. Such materials, which are defined as plies, are then stacked, according to a given sequence, to form a laminate which composes the skin of the composite panel.
Physical properties such as the buckling resistance and the stiffness of the panel are defined by the vertical arrangement of individual plies within the laminate. Such vertical arrangement is defined by the following design parameters: the number of plies, the order in which the positioning of plies having a determined orientation angle, the proportion of plies having an orientation angle defined with respect to the whole panel.
The composite panel is further composed of a group of zones which are submitted to various load cases and various dimension constraints, and it is thus necessary to define a vertical arrangement of plies for each panel zone.
It is then possible to modify such parameters so as to minimize the panel mass while increasing the structural performance of the panel.
Optimizing a laminated composite panel is however a complex problem as regards its solution as well as its definition which must take many feasibility criteria into account. As for aeronautical structures, for example, criteria of mass, stiffness, buckling resistance must be optimized while keeping in mind the design cost of such structures. Thus, the optimization process is a relatively complex combinatory problem because of the important number of variables and constraints involved and it also must take into account the calculation time.
The general approach consists in using a method for digitally optimizing the dimension and lay-up rules constraint parameters to reach the optimum solution(s).
A one-step optimization method is known, which uses a Genetic Algorithm (GA) based on a population of solutions which will evolve from generation to generation and get closer to the optimum solution. Such optimization method however implies a relatively important amount of time for evaluating all the calculation constraints. Therefore, the calculation time required for converging toward the optimum solution is not appropriate for industrial applications. As a matter of fact, the calculation time of Genetic Algorithms rapidly increases in time. Besides, the important number of lay-out rules generally entails a difficult convergence towards a proper solution.
An hybrid algorithm which combines the Genetic Algorithm and direct research is known. A master stack of plies which is applied to the whole panel is firstly determined using the GA. The number of plies to be positioned on each panel zone is then determined, using the direct research method. This method uses an approach to the optimization issue by assuming a simplified hypothesis about the ply loss rules which does not make it possible to render the real case of a composite panel.
A two-level optimization approach has recently been provided to solve the multi-criteria optimization issue, in which:
the number of plies per angle with the variable constraints is optimized to impart a continuity in thickness between adjacent zones,
the stacking sequence is locally optimized in parallel with an exchange of information between the optimization of two adjacent zones.
But this two-level approach does not make it possible to obtain ply continuity between two adjacent uniform thickness zones, therefore not industrially applicable.
It would be advantageous to provide an optimization method having simple design and operation, being time-saving and flexible as regards calculation, and making it possible to obtain an optimum arrangement of plies for the whole strengthened composite panel, while taking into account the criteria of structural stiffness and resistance, the laminate fabrication rules and the condition of ply continuity between two adjacent uniform thickness zones.